You are the second person I've heard suggest this. In my experience, though, it doesn't matter much. The snow is usually soft enough to simply lurch the snowshoe platform into the snow at a slight angle into the hill. Or, if you are shuffling quickly down the hill, lean the platform forward more. It is possible to get carried away and fall forward, but I haven't had it happen.
The big advantage of the pivoting section is on flat ground. When you lean forward, your foot goes into the snow before you have to pick it up. While going uphill, it is simply a bonus. You can take advantage of the pivot by placing the platform parallel to the slope and pivoting, so your foot is level. Doing that, however, places a lot of faith on the bars and spikes of the snowshoes. If you are using snowshoes without much in the way of bars and spikes, then you will slip backwards. On the other hand, if you take the approach I suggested for going downhill, and apply it for going uphill, then you will be more stable. In other words, slam the platform down (or into) the hill so that it is level.